Quantization of electromagnetic field in the Schwarzschild spacetime

Abstract

We discuss the problem of canonical quantization of electromagnetic field in the Schwarzschild spacetime. It is shown that a consistent procedure of canonical quantization of the field can be carried out without taking into account the internal region of the black hole. We prove that there exists a unitary gauge, which can be viewed as a combination of the Coulomb and Poincare gauges and is compatible with the field equations. The solutions corresponding to the stationary one-particle states of the electromagnetic field are studied, the canonical commutation relations and the Hamiltonian of the quantized electromagnetic field are obtained.

21 pages, 2 figures. v2: 3 references added, Introduction slightly enlarged, minor corrections in the rest of the text. v3: 1 reference removed, minor corrections in the text. v4: 1 reference added, minor corrections in the text